I was encountering the same annoying issue. This solution I followee may or may not be as useful (or correct) for all MacOS! I'm running Ventura 13.6 on an iMac
I exited Pub 2, located mru.dat and renamed it mru.dat.old (just in case I needed to retrieve it) and then opened Pub2, loaded and then saved/closed a pub 2 document and exited Pub2 again. I did not try just closing the document.
Then I opened Pub2 for a second time, looked at "Open Recent" and the document list was no longer empty (only showing the last file though).
I then opened Pub2 App'n Support via the Library and found a new mru.dat file as well as the old, renamed one which I've now deleted.
Loading a document via Finder works also (it appears in the list immediately) so it seems to be irrelevant how the document is loaded into Pub2.
It seems there is no need to re-boot the machine. Hope this helps. Sorry about all the I's.
Next stop: sorting Photo2 & Designer2